[Step-by-Step] Let X_1, X_2, ... be a sequence of independent random variables having distribution Exp;(θ). Let Y_n = min X_1, ..., X_n. Show that


Question: Let \(X_{1}, X_{2}, \ldots\) be a sequence of independent random variables having distribution \(\operatorname{Exp}(\theta)\). Let \(Y_{n} = \min \left\{X_{1}, \ldots, X_{n}\right\}\). Show that the sequence \(Y_{n}\) converges in probability and almost surely and find its limit.

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